It is known from Ohm's law that a voltage is developed across an electrically resistive device when current is passed therethrough. The value of the developed voltage is functionally related to (i) the resistance of the device and (ii) the amount of current through the device. If both the current and resistance values are relatively small, the developed voltage is small.
It is known in the art to use a differential amplifier for amplifying a voltage value developed across a device being monitored where the developed voltage value is small. Some known circuits use an integrated circuit, operational amplifier configured so as to function as a differential amplifier.
One problem with integrated circuit, differential amplifiers is the amplification of a common-mode voltage present at its inputs. If the inputs of the amplifier are connected together to make the differential voltage zero and the inputs are connected to a common-mode voltage value, the common-mode voltage value is amplified thereby causing a voltage signal to be present at the output of the amplifier. The value of this signal is directly proportional to the common-mode gain of the amplifier. The common-mode gain of an integrated circuit, differential amplifier is equal to the differential-mode gain of the amplifier divided by the common-mode rejection ratio of the amplifier. Thus, the signal at the output of the amplifier caused by the common-mode voltage present at its inputs varies inversely with the common-mode rejection ratio.
The common-mode rejection ratio of known integrated circuit, amplifiers is finite. Therefore, a variance in the value of the amplifier output signal resulting from the common-mode voltage cannot be ignored when the differential-mode gain of the amplifier circuit is relatively large. Use of a large gain, differential amplifier to amplify a DC voltage developed across a small impedance device results in an output signal that is not sufficiently accurate to permit a meaningful calculation of the resistance of the device.
Any changes in the value of the common-mode voltage present at the device being monitored causes changes in the value of the output signal of the differential amplifier. Also, components used to configure the integrated circuit, operational amplifier as a differential amplifier have their electrical characteristic specified within a tolerance value. As the actual characteristic values vary, the gain of the amplifier varies.
One particular art that uses a differential amplifier to monitor operativeness of an electrical device having a relatively small resistive value is automotive, air bag diagnostic circuits used in automotive, air bag systems. One component of an air bag system is known as a primer or squib. The primer "fires" when a sufficient amount of electrical current is passed therethrough. When the primer is "fired," a gas generating material is ignited to provide pressurized fluid to inflate an air bag. Typically, primers have a relatively small impedance of approximately one to four ohms.
U.S. Pat. No. 4,287,431 discloses an air bag diagnostic circuit used to monitor, among other things, the operativeness of a primer. In accordance with the '431 patent, an air bag system includes two, parallel-connected primers. The primers are connected to the vehicle battery through two inertia switches Each connection terminal of the primers has one inertia switch connected thereto Each inertia switch has an associated resistor connected thereacross. Each of the associated resistors has a resistance value substantially greater than the resistance value of the parallel-connected primers. An electrical test current having a value less than that required to "fire" the primers is established through the inertia switch resistors and through the primers This test current establishes a voltage across the primers
A diagnostic circuit is connected to the primers. The diagnostic circuit includes a differential amplifier having its two inputs connected to respective connection terminals of the primers. The output of the differential amplifier is an electrical signal having a value related to the value of the voltage developed across the primers.
If the primers are open circuited, the output of the differential amplifier is greater than a first predetermined value. If the primers are short circuited, the output of the differential amplifier is less than a second predetermined value. A comparator circuit is connected to the output of the differential amplifier. The comparator circuit provides a signal to actuate an indicator when the output of the differential amplifier indicates the primers are open or short circuited. The indicator warns the vehicle operator of a malfunction in the vehicle's air bag system. The diagnostic circuit disclosed in the '431 patent provides an indication of only extreme electrical conditions of the primers, i.e., the primers are open or short circuited.
Several factors exist in a circuit of the type disclosed in the '431 patent that prevent the differential amplifier output signal from being useful for accurately determining the resistance of the primers. Variations in the amplifier output signal can occur resulting from (i) variations in the differential voltage developed across the device or changes in the gain of the differential amplifier ("differential-mode errors"), and (ii) the presence of or changes in a common-mode voltage value at the inputs of the amplifier ("common-mode errors").
The output, Vout, of the differential amplifier disclosed in the '431 patent can be expressed as: EQU Vout=[(R15/R14)((R14+R16)/(R13+R15))]V2-(R16/R14)V1 (A)
where V1 is the voltage value at the input of resistor R14 and V2 is the voltage value at the input of resistor R13. Vcm is defined as the common-mode voltage present at the primers 2 and 3, and Vdiff is defined as the voltage value developed across the primers 2 and 3.
By definition: EQU V1=Vcm-1/2Vdiff, and (B) EQU V2=Vcm+1/2Vdiff (C)
Substituting equations (B) and (C) into equation (A) yields: EQU Vout=[(R15/R14)((R14+R16)/(R13+R15))](Vcm+1/2Vdiff)-(R16/R14)(Vcm-1/2Vdiff) (D)
Differential-mode errors arise when the gain resistors of the differential amplifier are mismatched, the values of the resistors associated with the inertia switches change, or the value of the battery voltage changes. These differential-mode errors cause Vdiff to vary which, in turn, causes Vout to vary.
Common-mode errors arise when a common-mode voltage value is present at the inputs of the differential amplifier, the common-mode voltage value at the inputs change because of changes in the values of resistors associated with the inertia switches, and the common-mode voltage value shifts because of changes in the value of the battery voltage. The presence of a common-mode voltage value plus changes in the common-mode voltage value causes uncertainty in the value of Vout. Because of these possible variances in the output voltage of the differential amplifier from both differential-mode errors and common-mode errors, the output signal of the differential amplifier is not useful for accurately determining the resistance value of the primers.
In the air bag art, an accurate measurement of the resistance value of the primers or squibs is useful to prevent false error signals from being provided by the air bag diagnostic circuit. Also, an accurate determination of the resistance value of the primers or squibs aids in determining which of any components are inoperative in the remainder of the air bag system.